Group-wise differentially private score histograms

This function computes two-dimensional principal component scores and releases group-wise differentially private histograms on a common score frame and grid. It is useful when observations have group labels and the low-dimensional score distribution should be compared across groups.

Usage

dp_score_group(
  X,
  group,
  eps,
  delta,
  bins,
  method = c("add", "sparse"),
  center = TRUE,
  standardize = FALSE,
  g_dppca = FALSE,
  cpp.option = FALSE,
  axes = c(1, 2)
)

Arguments

X: A matrix or data frame where rows correspond to observations and columns correspond to variables. X can additionally include a named column representing the group label for each observation.
group: Group labels. This can be a vector of length nrow(X) or a single column name in X. If a column name is supplied, that column is used as the group label and removed from the feature matrix.
eps: Positive number defining the total epsilon privacy parameter.
delta: Number in (0, 1) defining the total delta privacy parameter.
bins: Integer vector of length 2 defining the number of histogram bins along the first and second score axes, respectively.
method: Character vector specifying which private histogram methods to compute. Use "add" for the additive Gaussian histogram and "sparse" for the sparse thresholded histogram. The default is c("add", "sparse").
center: A logical value indicating whether to center the columns of X before computing principal component directions. The default is TRUE.
standardize: A logical value indicating whether to scale the columns of X by their sample standard deviations after optional centering. The default is FALSE.
g_dppca: A logical value indicating whether to use private principal component directions. The default is FALSE. See dp_pc_dir() for details.
cpp.option: A logical value passed to dp_pc_dir() when g_dppca = TRUE. The default is FALSE.
axes: Integer vector of length 2 specifying the principal components used to construct the score coordinates. The default is c(1, 2).

Value

A list with components:

score: An \(n \times 2\) matrix containing the PC scores for the two selected axes.
frame: A list with components xlim and ylim.
groups: A named list of group-specific histogram outputs.
method: Character vector of private histogram methods used.

Details

The score directions, plotting frame, and histogram grid are shared across all groups. For each group \(g\), the group-specific count in bin \(B_k\) is \(c_k^{(g)} = \sum_i 1\{s_i \in B_k, g_i = g\}\). Private histograms are then computed separately for each group on the common grid. Because the groups form a partition of the rows, the group-wise histograms use the same histogram privacy parameters for each group by parallel composition.

Examples

data(gau_g, package = "dppca")

# Compute private grouped PCA scores.
set.seed(123)
score_gau_g <- dp_score_group(
  gau_g,
  group = "group",
  eps = 3,
  delta = 1e-3,
  bins = c(8, 8)
)

head(score_gau_g$score)
#>            PC1        PC2
#> [1,] 0.5752441  0.9711984
#> [2,] 3.1987535  1.5765379
#> [3,] 2.0936989  1.0882390
#> [4,] 0.9725891  1.5285036
#> [5,] 1.0839100  0.4533152
#> [6,] 1.5430497 -1.0954815
head(score_gau_g$groups$group1$add)
#>          xmin        xmax     ymin      ymax        prob
#> 1 -13.6247864 -10.0056291 -13.7689 -10.14974 0.007860830
#> 2 -10.0056291  -6.3864719 -13.7689 -10.14974 0.000000000
#> 3  -6.3864719  -2.7673146 -13.7689 -10.14974 0.008186366
#> 4  -2.7673146   0.8518427 -13.7689 -10.14974 0.000000000
#> 5   0.8518427   4.4709999 -13.7689 -10.14974 0.000000000
#> 6   4.4709999   8.0901572 -13.7689 -10.14974 0.001209186